A particle confined in a rigid one-dimensional box (an infinite well) of length 17.0 fm has an energy level E_n = 2.0 MeV and an adjacent energy level E_n₊₁ = 37.5 MeV. What is the value of the ground state energy? (1 eV = 1.60 × 10^-19 J) A) 1.50 MeV B) 13.5 MeV C) 0.500 MeV D) 4.50 MeV

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Quizplus · Accepted Answer

The energy levels in an infinite well are given by:$$E_n = \frac{n^2 h^2}{8mL^2}$$where n is the principal quantum number, h is Planck's constant, m is the mass of the particle, and L is the length of the box.The difference in energy between two adjacent levels is:$$\Delta E = E_{n+1} - E_n = \frac{(n+1)^2 h^2}{8mL^2} - \frac{n^2 h^2}{8mL^2} = \frac{h^2}{8mL^2}$$Therefore, the ground state energy is:$$E_1 = E_n - \Delta E = 2.0 	ext{ MeV} - \frac{h^2}{8mL^2} = 1.50 	ext{ MeV}$$

A Particle Confined in a Rigid One-Dimensional Box (An Infinite